Please use this identifier to cite or link to this item: https://doi.org/2006/48185
Title: On the uncertainty inequality as applied to discrete signals
Authors: Venkatesh, Y.V. 
Raja, S.K.
Vidyasagar, G.
Issue Date: 2006
Source: Venkatesh, Y.V.,Raja, S.K.,Vidyasagar, G. (2006). On the uncertainty inequality as applied to discrete signals. International Journal of Mathematics and Mathematical Sciences 2006 : -. ScholarBank@NUS Repository. https://doi.org/2006/48185
Abstract: Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness) in the temporal/spectral domains of the (i) continuous-time and (ii) discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product of effective temporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem: for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using the standard definitions of the temporal and spectral spreads of the signal? In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
Source Title: International Journal of Mathematics and Mathematical Sciences
URI: http://scholarbank.nus.edu.sg/handle/10635/56908
ISSN: 01611712
DOI: 2006/48185
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